David Miliband today calls for the government to withdraw a £100m taxpayer subsidy to private schools as part of its deficit reduction programme.

The Labour leadership contender and former education minister makes his proposal in an article for the Guardian setting out his tests for the government's budget next week.

He writes: "Under the Tories, the poorest will end up paying the price of the mistakes of the richest. We should not be afraid of the mansion tax on £2m houses or extending the bankers' bonus tax, rather than charging the poorest with VAT rises. And the idea of taking money from the poorest children while continuing to subsidise private schools is just wrong."

Under the Charities Act 2006, independent schools and private hospitals are given charitable status in return for providing public benefit, including access to facilities for local people and providing means-tested bursaries.

It is permissible for public schools to charge fees for these services as long as there is, on balance, an effort to help poor and local people. The tax relief is, on average, worth £225 per child each year to private schools, or just under 2.5% of their average annual turnover.

Under new rules, officials from the Charity Commission can inspect independent schools to ensure they provide public benefit; schools that fail the test can be stripped of charitable status. There have been reports that the schools secretary, Michael Gove, may be planning to go in the opposite direction by softening demands to provide more bursaries to pupils from poor families.

Miliband's remarks came as Gillian Lowe, president of the Girls' Schools Association, claimed that many headteachers in the private sector were leaving their posts because of a prevailing image that private schools were elitist.

One of Miliband's rivals for the Labour leadership, Ed Balls, today made his own attack on the coalition prior to the budget, launching an online petition called "stop the VAT bombshell" – using an image of Nick Clegg with a Lib Dem poster which that party ran in the election. The Lib Dems campaigned against a VAT rise, quoting the cost of the VAT "bombshell" to each family. Now Balls wants the Lib Dems to reject a budget VAT rise as regressive and hitting the poor hardest.

Balls said: "I believe it would be economic madness for George Osborne to go ahead with deflationary spending cuts and the VAT hike that his advisers have been whispering about to the newspapers. I fear this 'unemployment budget' will set back the economic recovery and put jobs at risk. In 1993, the Labour opposition …succeeded in voting down the budget over the plans drawn up by Norman Lamont and David Cameron to impose the maximum rate of VAT on domestic fuel and power. Now the stakes are even higher, and our opposition must be equally robust."

A third Labour contender, Diane Abbott, today defended her decision to send her son to a fee-paying school.

Abbott, MP for Hackney North (where Labour poured in money to improve secondary education, with a wave of academies) sent her son James to the City of London school. She had previously said her decision was intellectually incoherent, but now claims that, since local schooling had improved, she would now have chosen a state school: "I was taught you sacrifice everything for your child. I could have joined the church, and all the stuff people do, but I was not prepared to do so. That school was the making of him."